WOLFRAM|DEMONSTRATIONS PROJECT

The Causal Interpretation of Exciting an Atom by Absorption of Intense Light

​
time steps
401
perturbation potential
0.2
frequency correction factor
0.55
The process of exciting an atom involves adding energy. In the photoelectric effect, electrons are emitted when they absorb energy from incident radiation with a certain minimum frequency
ω
. This Demonstration shows only the energy transition of a perturbed atom. An atom is described by a wave in a box with infinitely high walls. For this particular case, the atom is perturbed by a strong periodic external potential, which could be interpreted as a weak or intense electric field with an electric field strength
E
0
that oscillates with some angular frequency
ω
. The absorption (or emission) of energy could be described by the transition frequency
ω
of the adjacent quantum energy
level
E
n
, which is
ω=
ω
n
-
ω
n-1
=(
E
n
-
E
n-1
)/ℏ=

λ
ℏ
2(2n-1)
π
2m
2
L
(here, with frequency correction factor
λ'
, mass
m=1
,
ℏ=1
, box length
L=1
, and energy eigenvalue
n
). Only for definite values of the frequency
ω
(by a given strength
E
0
of the perturbation), depending on the energy eigenvalues
n=1,2,3,…
, can the atom undergo a transition from the first to the second excited state. If the perturbation term
E
0
becomes large, the quantum state evolves into a superposition of states with different energy. These mixed states lead to ergodic motion of the quantum particle. The excited atom can be measured by removing the confining well; then the particle moves away faster because of the excited state. The simplicity of the model neglects quantization of the transition-inducing field and other radiation effects.
In the causal interpretation, the particle position is well-defined and the situation is described by a wavefunction (and a quantum potential) that evolves continuously according to the Schrödinger equation and by the particle positions that change continuously according to the guiding equation.
The trajectories are given as curves along the velocity field given by the quantum current. While the particle positions are measurable in the usual way (the statistics are given by
2
ψ
), a normal position measurement always disturbs the trajectory. Therefore the undisturbed trajectories cannot be measured in the usual way by performing several position measurements in short time intervals. In the causal interpretation there is no evidence of quantum jumps.
The trajectories are positioned in
(x,t)
space. The initial positions of the particles are linearly distributed around the peak inside the wave. The graphic on the right shows the squared wavefunction, the potential, and the possible trajectories. The graphic on the left shows the particles' positions, the squared wavefunction (orange), the quantum potential (red), and the potential (blue). The potentials are approximately scaled to fit.